Eigenvalues in Riemannian GeometryAcademic Press, 07.11.1984 - 362 Seiten The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery. |
Inhalt
| 1 | |
| 26 | |
Chapter III λ1 and Curvature | 55 |
Chapter IV Isoperimetric Inequalities | 85 |
Chapter V Eigenvalues and the Kinematic Measure | 113 |
Chapter VI The Heat Kernel for Compact Manifolds | 134 |
Chapter VII The Dirichlet Heat Kernel for Regular Domains | 158 |
Chapter VIII The Heat Kernel for Noncompact Manifolds | 179 |
Chapter X Surfaces of Constant Negative Curvature | 239 |
Chapter XI The Selberg Trace Formula | 266 |
Chapter XII Miscellanea | 303 |
Laplacian on Forms | 334 |
Bibliography | 345 |
| 359 | |
Pure and Applied Mathematics | 363 |
Chapter IX Topological Perturbations with Negligible Effect | 207 |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
argument boundary Cheeger closed geodesic compact closure compact Riemannian manifold compact support consider const constant sectional curvature continuous function convergence dA(w define denote diffeomorphic differential Dirichlet eigenvalue problem Dirichlet heat kernel dV(x dV(y easily eigenfunction equality estimate Euclidean exists finite fixed follows function f fundamental solution geodesic disk geometric given grad ƒ Green's formula heat equation heat kernel hyperbolic hyperplane implies integral intersection isometry isoperimetric inequality Jacobi field L²(M Laplacian LEMMA lower bound n-dimensional Neumann eigenvalue nodal domain nontrivial obtain orthogonal orthonormal P₁ positive constant PROOF OF THEOREM radius regular domain result Ricci curvature Riemann surface Riemannian manifold Riemannian metric satisfying sectional curvature sinh submanifolds tangent trace formula transformation upper bound valid vanishing vector field zero
Verweise auf dieses Buch
Riemannian Geometry Sylvestre Gallot,Dominique Hulin,Jacques Lafontaine Eingeschränkte Leseprobe - 2004 |